/*-
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef UV_TREE_H_
#define UV_TREE_H_

#ifndef UV__UNUSED
#if __GNUC__
#define UV__UNUSED __attribute__((unused))
#else
#define UV__UNUSED
#endif
#endif

/*
 * This file defines data structures for different types of trees:
 * splay trees and red-black trees.
 *
 * A splay tree is a self-organizing data structure.  Every operation
 * on the tree causes a splay to happen.  The splay moves the requested
 * node to the root of the tree and partly rebalances it.
 *
 * This has the benefit that request locality causes faster lookups as
 * the requested nodes move to the top of the tree.  On the other hand,
 * every lookup causes memory writes.
 *
 * The Balance Theorem bounds the total access time for m operations
 * and n inserts on an initially empty tree as O((m + n)lg n).  The
 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *  - every search path from the root to a leaf consists of the
 *    same number of black nodes,
 *  - each red node (except for the root) has a black parent,
 *  - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

#define SPLAY_HEAD(name, type) \
  struct name { \
    struct type* sph_root; /* root of the tree */ \
  }

#define SPLAY_INITIALIZER(root) \
  { NULL }

#define SPLAY_INIT(root) \
  do { \
    (root)->sph_root = NULL; \
  } while (/*CONSTCOND*/ 0)

#define SPLAY_ENTRY(type) \
  struct { \
    struct type* spe_left; /* left element */ \
    struct type* spe_right; /* right element */ \
  }

#define SPLAY_LEFT(elm, field) (elm)->field.spe_left
#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
#define SPLAY_ROOT(head) (head)->sph_root
#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field) \
  do { \
    SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
    SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
    (head)->sph_root = tmp; \
  } while (/*CONSTCOND*/ 0)

#define SPLAY_ROTATE_LEFT(head, tmp, field) \
  do { \
    SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
    SPLAY_LEFT(tmp, field) = (head)->sph_root; \
    (head)->sph_root = tmp; \
  } while (/*CONSTCOND*/ 0)

#define SPLAY_LINKLEFT(head, tmp, field) \
  do { \
    SPLAY_LEFT(tmp, field) = (head)->sph_root; \
    tmp = (head)->sph_root; \
    (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
  } while (/*CONSTCOND*/ 0)

#define SPLAY_LINKRIGHT(head, tmp, field) \
  do { \
    SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
    tmp = (head)->sph_root; \
    (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
  } while (/*CONSTCOND*/ 0)

#define SPLAY_ASSEMBLE(head, node, left, right, field) \
  do { \
    SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
    SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field); \
    SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
    SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
  } while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp) \
  void name##_SPLAY(struct name*, struct type*); \
  void name##_SPLAY_MINMAX(struct name*, int); \
  struct type* name##_SPLAY_INSERT(struct name*, struct type*); \
  struct type* name##_SPLAY_REMOVE(struct name*, struct type*); \
\
  /* Finds the node with the same key as elm */ \
  static __inline struct type* \
      name##_SPLAY_FIND(struct name* head, struct type* elm) { \
    if (SPLAY_EMPTY(head)) \
      return (NULL); \
    name##_SPLAY(head, elm); \
    if ((cmp)(elm, (head)->sph_root) == 0) \
      return (head->sph_root); \
    return (NULL); \
  } \
\
  static __inline struct type* \
      name##_SPLAY_NEXT(struct name* head, struct type* elm) { \
    name##_SPLAY(head, elm); \
    if (SPLAY_RIGHT(elm, field) != NULL) { \
      elm = SPLAY_RIGHT(elm, field); \
      while (SPLAY_LEFT(elm, field) != NULL) { \
        elm = SPLAY_LEFT(elm, field); \
      } \
    } else \
      elm = NULL; \
    return (elm); \
  } \
\
  static __inline struct type* \
      name##_SPLAY_MIN_MAX(struct name* head, int val) { \
    name##_SPLAY_MINMAX(head, val); \
    return (SPLAY_ROOT(head)); \
  }

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp) \
  struct type* \
      name##_SPLAY_INSERT(struct name* head, struct type* elm) { \
    if (SPLAY_EMPTY(head)) { \
      SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
    } else { \
      int __comp; \
      name##_SPLAY(head, elm); \
      __comp = (cmp)(elm, (head)->sph_root); \
      if (__comp < 0) { \
        SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field); \
        SPLAY_RIGHT(elm, field) = (head)->sph_root; \
        SPLAY_LEFT((head)->sph_root, field) = NULL; \
      } else if (__comp > 0) { \
        SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field); \
        SPLAY_LEFT(elm, field) = (head)->sph_root; \
        SPLAY_RIGHT((head)->sph_root, field) = NULL; \
      } else \
        return ((head)->sph_root); \
    } \
    (head)->sph_root = (elm); \
    return (NULL); \
  } \
\
  struct type* \
      name##_SPLAY_REMOVE(struct name* head, struct type* elm) { \
    struct type* __tmp; \
    if (SPLAY_EMPTY(head)) \
      return (NULL); \
    name##_SPLAY(head, elm); \
    if ((cmp)(elm, (head)->sph_root) == 0) { \
      if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
        (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
      } else { \
        __tmp = SPLAY_RIGHT((head)->sph_root, field); \
        (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
        name##_SPLAY(head, elm); \
        SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
      } \
      return (elm); \
    } \
    return (NULL); \
  } \
\
  void \
      name##_SPLAY(struct name* head, struct type* elm) { \
    struct type __node, *__left, *__right, *__tmp; \
    int __comp; \
\
    SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL; \
    __left = __right = &__node; \
\
    while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
      if (__comp < 0) { \
        __tmp = SPLAY_LEFT((head)->sph_root, field); \
        if (__tmp == NULL) \
          break; \
        if ((cmp)(elm, __tmp) < 0) { \
          SPLAY_ROTATE_RIGHT(head, __tmp, field); \
          if (SPLAY_LEFT((head)->sph_root, field) == NULL) \
            break; \
        } \
        SPLAY_LINKLEFT(head, __right, field); \
      } else if (__comp > 0) { \
        __tmp = SPLAY_RIGHT((head)->sph_root, field); \
        if (__tmp == NULL) \
          break; \
        if ((cmp)(elm, __tmp) > 0) { \
          SPLAY_ROTATE_LEFT(head, __tmp, field); \
          if (SPLAY_RIGHT((head)->sph_root, field) == NULL) \
            break; \
        } \
        SPLAY_LINKRIGHT(head, __left, field); \
      } \
    } \
    SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
  } \
\
  /* Splay with either the minimum or the maximum element \
   * Used to find minimum or maximum element in tree. \
   */ \
  void name##_SPLAY_MINMAX(struct name* head, int __comp) { \
    struct type __node, *__left, *__right, *__tmp; \
\
    SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL; \
    __left = __right = &__node; \
\
    while (1) { \
      if (__comp < 0) { \
        __tmp = SPLAY_LEFT((head)->sph_root, field); \
        if (__tmp == NULL) \
          break; \
        if (__comp < 0) { \
          SPLAY_ROTATE_RIGHT(head, __tmp, field); \
          if (SPLAY_LEFT((head)->sph_root, field) == NULL) \
            break; \
        } \
        SPLAY_LINKLEFT(head, __right, field); \
      } else if (__comp > 0) { \
        __tmp = SPLAY_RIGHT((head)->sph_root, field); \
        if (__tmp == NULL) \
          break; \
        if (__comp > 0) { \
          SPLAY_ROTATE_LEFT(head, __tmp, field); \
          if (SPLAY_RIGHT((head)->sph_root, field) == NULL) \
            break; \
        } \
        SPLAY_LINKRIGHT(head, __left, field); \
      } \
    } \
    SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
  }

#define SPLAY_NEGINF -1
#define SPLAY_INF 1

#define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL : name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head) \
  for ((x) = SPLAY_MIN(name, head); \
       (x) != NULL; \
       (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-black tree */
#define RB_HEAD(name, type) \
  struct name { \
    struct type* rbh_root; /* root of the tree */ \
  }

#define RB_INITIALIZER(root) \
  { NULL }

#define RB_INIT(root) \
  do { \
    (root)->rbh_root = NULL; \
  } while (/*CONSTCOND*/ 0)

#define RB_BLACK 0
#define RB_RED 1
#define RB_ENTRY(type) \
  struct { \
    struct type* rbe_left; /* left element */ \
    struct type* rbe_right; /* right element */ \
    struct type* rbe_parent; /* parent element */ \
    int rbe_color; /* node color */ \
  }

#define RB_LEFT(elm, field) (elm)->field.rbe_left
#define RB_RIGHT(elm, field) (elm)->field.rbe_right
#define RB_PARENT(elm, field) (elm)->field.rbe_parent
#define RB_COLOR(elm, field) (elm)->field.rbe_color
#define RB_ROOT(head) (head)->rbh_root
#define RB_EMPTY(head) (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field) \
  do { \
    RB_PARENT(elm, field) = parent; \
    RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
    RB_COLOR(elm, field) = RB_RED; \
  } while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(black, red, field) \
  do { \
    RB_COLOR(black, field) = RB_BLACK; \
    RB_COLOR(red, field) = RB_RED; \
  } while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x) \
  do { \
  } while (0)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field) \
  do { \
    (tmp) = RB_RIGHT(elm, field); \
    if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
      RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
    } \
    RB_AUGMENT(elm); \
    if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
      if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
        RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
      else \
        RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
    } else \
      (head)->rbh_root = (tmp); \
    RB_LEFT(tmp, field) = (elm); \
    RB_PARENT(elm, field) = (tmp); \
    RB_AUGMENT(tmp); \
    if ((RB_PARENT(tmp, field))) \
      RB_AUGMENT(RB_PARENT(tmp, field)); \
  } while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) \
  do { \
    (tmp) = RB_LEFT(elm, field); \
    if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
      RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
    } \
    RB_AUGMENT(elm); \
    if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
      if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
        RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
      else \
        RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
    } else \
      (head)->rbh_root = (tmp); \
    RB_RIGHT(tmp, field) = (elm); \
    RB_PARENT(elm, field) = (tmp); \
    RB_AUGMENT(tmp); \
    if ((RB_PARENT(tmp, field))) \
      RB_AUGMENT(RB_PARENT(tmp, field)); \
  } while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp) \
  RB_PROTOTYPE_INTERNAL(name, type, field, cmp, )
#define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
  RB_PROTOTYPE_INTERNAL(name, type, field, cmp, UV__UNUSED static)
#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
  attr void name##_RB_INSERT_COLOR(struct name*, struct type*); \
  attr void name##_RB_REMOVE_COLOR(struct name*, struct type*, struct type*); \
  attr struct type* name##_RB_REMOVE(struct name*, struct type*); \
  attr struct type* name##_RB_INSERT(struct name*, struct type*); \
  attr struct type* name##_RB_FIND(struct name*, struct type*); \
  attr struct type* name##_RB_NFIND(struct name*, struct type*); \
  attr struct type* name##_RB_NEXT(struct type*); \
  attr struct type* name##_RB_PREV(struct type*); \
  attr struct type* name##_RB_MINMAX(struct name*, int);

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define RB_GENERATE(name, type, field, cmp) \
  RB_GENERATE_INTERNAL(name, type, field, cmp, )
#define RB_GENERATE_STATIC(name, type, field, cmp) \
  RB_GENERATE_INTERNAL(name, type, field, cmp, UV__UNUSED static)
#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
  attr void \
      name##_RB_INSERT_COLOR(struct name* head, struct type* elm) { \
    struct type *parent, *gparent, *tmp; \
    while ((parent = RB_PARENT(elm, field)) != NULL && \
           RB_COLOR(parent, field) == RB_RED) { \
      gparent = RB_PARENT(parent, field); \
      if (parent == RB_LEFT(gparent, field)) { \
        tmp = RB_RIGHT(gparent, field); \
        if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
          RB_COLOR(tmp, field) = RB_BLACK; \
          RB_SET_BLACKRED(parent, gparent, field); \
          elm = gparent; \
          continue; \
        } \
        if (RB_RIGHT(parent, field) == elm) { \
          RB_ROTATE_LEFT(head, parent, tmp, field); \
          tmp = parent; \
          parent = elm; \
          elm = tmp; \
        } \
        RB_SET_BLACKRED(parent, gparent, field); \
        RB_ROTATE_RIGHT(head, gparent, tmp, field); \
      } else { \
        tmp = RB_LEFT(gparent, field); \
        if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
          RB_COLOR(tmp, field) = RB_BLACK; \
          RB_SET_BLACKRED(parent, gparent, field); \
          elm = gparent; \
          continue; \
        } \
        if (RB_LEFT(parent, field) == elm) { \
          RB_ROTATE_RIGHT(head, parent, tmp, field); \
          tmp = parent; \
          parent = elm; \
          elm = tmp; \
        } \
        RB_SET_BLACKRED(parent, gparent, field); \
        RB_ROTATE_LEFT(head, gparent, tmp, field); \
      } \
    } \
    RB_COLOR(head->rbh_root, field) = RB_BLACK; \
  } \
\
  attr void \
      name##_RB_REMOVE_COLOR(struct name* head, struct type* parent, struct type* elm) { \
    struct type* tmp; \
    while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
           elm != RB_ROOT(head)) { \
      if (RB_LEFT(parent, field) == elm) { \
        tmp = RB_RIGHT(parent, field); \
        if (RB_COLOR(tmp, field) == RB_RED) { \
          RB_SET_BLACKRED(tmp, parent, field); \
          RB_ROTATE_LEFT(head, parent, tmp, field); \
          tmp = RB_RIGHT(parent, field); \
        } \
        if ((RB_LEFT(tmp, field) == NULL || \
             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) && \
            (RB_RIGHT(tmp, field) == NULL || \
             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) { \
          RB_COLOR(tmp, field) = RB_RED; \
          elm = parent; \
          parent = RB_PARENT(elm, field); \
        } else { \
          if (RB_RIGHT(tmp, field) == NULL || \
              RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) { \
            struct type* oleft; \
            if ((oleft = RB_LEFT(tmp, field)) != NULL) \
              RB_COLOR(oleft, field) = RB_BLACK; \
            RB_COLOR(tmp, field) = RB_RED; \
            RB_ROTATE_RIGHT(head, tmp, oleft, field); \
            tmp = RB_RIGHT(parent, field); \
          } \
          RB_COLOR(tmp, field) = RB_COLOR(parent, field); \
          RB_COLOR(parent, field) = RB_BLACK; \
          if (RB_RIGHT(tmp, field)) \
            RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK; \
          RB_ROTATE_LEFT(head, parent, tmp, field); \
          elm = RB_ROOT(head); \
          break; \
        } \
      } else { \
        tmp = RB_LEFT(parent, field); \
        if (RB_COLOR(tmp, field) == RB_RED) { \
          RB_SET_BLACKRED(tmp, parent, field); \
          RB_ROTATE_RIGHT(head, parent, tmp, field); \
          tmp = RB_LEFT(parent, field); \
        } \
        if ((RB_LEFT(tmp, field) == NULL || \
             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) && \
            (RB_RIGHT(tmp, field) == NULL || \
             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) { \
          RB_COLOR(tmp, field) = RB_RED; \
          elm = parent; \
          parent = RB_PARENT(elm, field); \
        } else { \
          if (RB_LEFT(tmp, field) == NULL || \
              RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) { \
            struct type* oright; \
            if ((oright = RB_RIGHT(tmp, field)) != NULL) \
              RB_COLOR(oright, field) = RB_BLACK; \
            RB_COLOR(tmp, field) = RB_RED; \
            RB_ROTATE_LEFT(head, tmp, oright, field); \
            tmp = RB_LEFT(parent, field); \
          } \
          RB_COLOR(tmp, field) = RB_COLOR(parent, field); \
          RB_COLOR(parent, field) = RB_BLACK; \
          if (RB_LEFT(tmp, field)) \
            RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK; \
          RB_ROTATE_RIGHT(head, parent, tmp, field); \
          elm = RB_ROOT(head); \
          break; \
        } \
      } \
    } \
    if (elm) \
      RB_COLOR(elm, field) = RB_BLACK; \
  } \
\
  attr struct type* \
      name##_RB_REMOVE(struct name* head, struct type* elm) { \
    struct type *child, *parent, *old = elm; \
    int color; \
    if (RB_LEFT(elm, field) == NULL) \
      child = RB_RIGHT(elm, field); \
    else if (RB_RIGHT(elm, field) == NULL) \
      child = RB_LEFT(elm, field); \
    else { \
      struct type* left; \
      elm = RB_RIGHT(elm, field); \
      while ((left = RB_LEFT(elm, field)) != NULL) \
        elm = left; \
      child = RB_RIGHT(elm, field); \
      parent = RB_PARENT(elm, field); \
      color = RB_COLOR(elm, field); \
      if (child) \
        RB_PARENT(child, field) = parent; \
      if (parent) { \
        if (RB_LEFT(parent, field) == elm) \
          RB_LEFT(parent, field) = child; \
        else \
          RB_RIGHT(parent, field) = child; \
        RB_AUGMENT(parent); \
      } else \
        RB_ROOT(head) = child; \
      if (RB_PARENT(elm, field) == old) \
        parent = elm; \
      (elm)->field = (old)->field; \
      if (RB_PARENT(old, field)) { \
        if (RB_LEFT(RB_PARENT(old, field), field) == old) \
          RB_LEFT(RB_PARENT(old, field), field) = elm; \
        else \
          RB_RIGHT(RB_PARENT(old, field), field) = elm; \
        RB_AUGMENT(RB_PARENT(old, field)); \
      } else \
        RB_ROOT(head) = elm; \
      RB_PARENT(RB_LEFT(old, field), field) = elm; \
      if (RB_RIGHT(old, field)) \
        RB_PARENT(RB_RIGHT(old, field), field) = elm; \
      if (parent) { \
        left = parent; \
        do { \
          RB_AUGMENT(left); \
        } while ((left = RB_PARENT(left, field)) != NULL); \
      } \
      goto color; \
    } \
    parent = RB_PARENT(elm, field); \
    color = RB_COLOR(elm, field); \
    if (child) \
      RB_PARENT(child, field) = parent; \
    if (parent) { \
      if (RB_LEFT(parent, field) == elm) \
        RB_LEFT(parent, field) = child; \
      else \
        RB_RIGHT(parent, field) = child; \
      RB_AUGMENT(parent); \
    } else \
      RB_ROOT(head) = child; \
  color: \
    if (color == RB_BLACK) \
      name##_RB_REMOVE_COLOR(head, parent, child); \
    return (old); \
  } \
\
  /* Inserts a node into the RB tree */ \
  attr struct type* \
      name##_RB_INSERT(struct name* head, struct type* elm) { \
    struct type* tmp; \
    struct type* parent = NULL; \
    int comp = 0; \
    tmp = RB_ROOT(head); \
    while (tmp) { \
      parent = tmp; \
      comp = (cmp)(elm, parent); \
      if (comp < 0) \
        tmp = RB_LEFT(tmp, field); \
      else if (comp > 0) \
        tmp = RB_RIGHT(tmp, field); \
      else \
        return (tmp); \
    } \
    RB_SET(elm, parent, field); \
    if (parent != NULL) { \
      if (comp < 0) \
        RB_LEFT(parent, field) = elm; \
      else \
        RB_RIGHT(parent, field) = elm; \
      RB_AUGMENT(parent); \
    } else \
      RB_ROOT(head) = elm; \
    name##_RB_INSERT_COLOR(head, elm); \
    return (NULL); \
  } \
\
  /* Finds the node with the same key as elm */ \
  attr struct type* \
      name##_RB_FIND(struct name* head, struct type* elm) { \
    struct type* tmp = RB_ROOT(head); \
    int comp; \
    while (tmp) { \
      comp = cmp(elm, tmp); \
      if (comp < 0) \
        tmp = RB_LEFT(tmp, field); \
      else if (comp > 0) \
        tmp = RB_RIGHT(tmp, field); \
      else \
        return (tmp); \
    } \
    return (NULL); \
  } \
\
  /* Finds the first node greater than or equal to the search key */ \
  attr struct type* \
      name##_RB_NFIND(struct name* head, struct type* elm) { \
    struct type* tmp = RB_ROOT(head); \
    struct type* res = NULL; \
    int comp; \
    while (tmp) { \
      comp = cmp(elm, tmp); \
      if (comp < 0) { \
        res = tmp; \
        tmp = RB_LEFT(tmp, field); \
      } else if (comp > 0) \
        tmp = RB_RIGHT(tmp, field); \
      else \
        return (tmp); \
    } \
    return (res); \
  } \
\
  /* ARGSUSED */ \
  attr struct type* \
      name##_RB_NEXT(struct type* elm) { \
    if (RB_RIGHT(elm, field)) { \
      elm = RB_RIGHT(elm, field); \
      while (RB_LEFT(elm, field)) \
        elm = RB_LEFT(elm, field); \
    } else { \
      if (RB_PARENT(elm, field) && \
          (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
        elm = RB_PARENT(elm, field); \
      else { \
        while (RB_PARENT(elm, field) && \
               (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
          elm = RB_PARENT(elm, field); \
        elm = RB_PARENT(elm, field); \
      } \
    } \
    return (elm); \
  } \
\
  /* ARGSUSED */ \
  attr struct type* \
      name##_RB_PREV(struct type* elm) { \
    if (RB_LEFT(elm, field)) { \
      elm = RB_LEFT(elm, field); \
      while (RB_RIGHT(elm, field)) \
        elm = RB_RIGHT(elm, field); \
    } else { \
      if (RB_PARENT(elm, field) && \
          (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
        elm = RB_PARENT(elm, field); \
      else { \
        while (RB_PARENT(elm, field) && \
               (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
          elm = RB_PARENT(elm, field); \
        elm = RB_PARENT(elm, field); \
      } \
    } \
    return (elm); \
  } \
\
  attr struct type* \
      name##_RB_MINMAX(struct name* head, int val) { \
    struct type* tmp = RB_ROOT(head); \
    struct type* parent = NULL; \
    while (tmp) { \
      parent = tmp; \
      if (val < 0) \
        tmp = RB_LEFT(tmp, field); \
      else \
        tmp = RB_RIGHT(tmp, field); \
    } \
    return (parent); \
  }

#define RB_NEGINF -1
#define RB_INF 1

#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
#define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
#define RB_PREV(name, x, y) name##_RB_PREV(y)
#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head) \
  for ((x) = RB_MIN(name, head); \
       (x) != NULL; \
       (x) = name##_RB_NEXT(x))

#define RB_FOREACH_FROM(x, name, y) \
  for ((x) = (y); \
       ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
       (x) = (y))

#define RB_FOREACH_SAFE(x, name, head, y) \
  for ((x) = RB_MIN(name, head); \
       ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
       (x) = (y))

#define RB_FOREACH_REVERSE(x, name, head) \
  for ((x) = RB_MAX(name, head); \
       (x) != NULL; \
       (x) = name##_RB_PREV(x))

#define RB_FOREACH_REVERSE_FROM(x, name, y) \
  for ((x) = (y); \
       ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
       (x) = (y))

#define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
  for ((x) = RB_MAX(name, head); \
       ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
       (x) = (y))

#endif /* UV_TREE_H_ */
